000132326 001__ 132326 000132326 005__ 20241125101156.0 000132326 0247_ $$2doi$$a10.1016/j.apnum.2023.09.008 000132326 0248_ $$2sideral$$a137478 000132326 037__ $$aART-2023-137478 000132326 041__ $$aeng 000132326 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, M.$$uUniversidad de Zaragoza 000132326 245__ $$aExplicit two-step peer methods with reused stages 000132326 260__ $$c2023 000132326 5060_ $$aAccess copy available to the general public$$fUnrestricted 000132326 5203_ $$aTwo-step peer methods for the numerical solution of Initial Value Problems (IVP) combine the advantages of Runge-Kutta (RK) and multistep methods to obtain high stage order and provide in a natural way a dense output. In general, explicit s-stage peer methods require s evaluations of the vector field at each step. Nevertheless, Klinge and coworkers (BIT Numer Math, 2018) have shown that some methods use less function calls se<s, here called effective stages, by re-using sr=s−se previously computed stages (shifted stages) from the previous steps in the current one. In this paper we propose a new approach, different from the one used by Klinge and coworkers, to re-use previously computed stages, that we call peer methods with reused stages, showing that methods with reused stages and se effective stages are equivalent to three-step peer methods with se stages. Then, we analyze all the families of methods with two effective stages, obtaining methods with s=3 and orders 4 and 5 in which the free parameters of the families have been used to minimize the coefficient of the leading error term as well as to maximize the absolute stability interval. We have also studied one family of peer methods with s=4 and three effective stages, obtaining a method with order 6, superconvergent of order 7, and optimized leading error term as well as absolute stability interval. Some numerical experiments show the performance of the obtained methods by comparing them with other previously obtained peer methods as well as other standard Runge-Kutta and multistep methods. 000132326 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31 000132326 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000132326 590__ $$a2.2$$b2023 000132326 592__ $$a1.006$$b2023 000132326 591__ $$aMATHEMATICS, APPLIED$$b46 / 332 = 0.139$$c2023$$dQ1$$eT1 000132326 593__ $$aApplied Mathematics$$c2023$$dQ1 000132326 593__ $$aNumerical Analysis$$c2023$$dQ1 000132326 593__ $$aComputational Mathematics$$c2023$$dQ1 000132326 594__ $$a5.6$$b2023 000132326 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000132326 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, J.I.$$uUniversidad de Zaragoza 000132326 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza 000132326 700__ $$aSaenz de la Torre, A. 000132326 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000132326 773__ $$g195 (2023), 75-88$$pAppl. numer. math.$$tAPPLIED NUMERICAL MATHEMATICS$$x0168-9274 000132326 8564_ $$s357871$$uhttps://zaguan.unizar.es/record/132326/files/texto_completo.pdf$$yPreprint 000132326 8564_ $$s1391802$$uhttps://zaguan.unizar.es/record/132326/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000132326 909CO $$ooai:zaguan.unizar.es:132326$$particulos$$pdriver 000132326 951__ $$a2024-11-22-12:09:18 000132326 980__ $$aARTICLE